wiktionary projection projector projective tocright Projection , projector , or projective may refer to The display of an image by devices such as Movie projector Video projector Overhead projector Slide projector Camera obscura Projection screen Map projection , reduces a three dimensional planet to a flat map geography Graphical projection , the production of a two dimensional image of a three dimensional object Parallel projection Orthographic projection , including Plan view Plan , or floor plan ... , a view of the interior at a particular cutting plane Axonometric projection , including Isometric projection Dimetric projection Trimetric projection Oblique projection , including Cabinet projection Cavalier projection Perspective projection anchor chemistry Chemistry Fischer projection Haworth projection Newman projection Natta projection Mathematics Projection mathematics , any of several different types of functions, mappings, operations, or transformations 3D projectionProjection relational algebra Projection linear algebra Vector projectionProjection method fluid dynamics Projection ... direction, projective module s and projective object s generalize free modules Other Projection alchemy , process in Alchemy Projection areas , areas of the brain where sensory processing occurs Military power projection , the capacity of a state to implement policy by means of force, or the threat thereof, in an area distant from its own territory Psychological projection , or Freudian projection ..., thoughts, or emotions Projection fibers , in neuroscience, white matter fibers that connect ... developments based on current statistics and trends Projection music , acoustical phenomenon whereby ... and Acoustics Publ. Springer, New York, 2010 See also lookfrom intitle Project disambiguation Projection effect disambiguation disambig de Projektion eo Projekcio fr Projection ko it Proiezione he nl Projectie ja no Projeksjon pl Projekcja pt Proje o ru simple Projection sl Projekcija ... more details
Projection effect may refer to Front projection effect , in camera visual effect Rear projection effect , in camera visual effect Insolation Projection effect , the amount of sunlight onto a portion of the Earth relative to its tilt In astronomy, a type of observational illusion caused by viewing distant objects or phenomenon from a particular perspective. Examples include superluminal motion , the retrograde motion of the planets, and optical double stars. See also Projection disambiguation Effect disambiguation dab ... more details
File Behrmann projection SW.jpg 450px thumb Behrmann projection of the world. Image Tissot indicatrix world map Behrmann equal area proj.svg 450px thumb upright 2.2 right The Behrmann cylindrical equal area projection with Tissot s indicatrix Tissot s indicatrices of deformation The Behrmann projection is a Map projection Cylindrical cylindrical map projection . This is an orthographic projection onto a cylinder secant at the 30 parallels. It is equal area, but distortion of shape increases with distance from the standard parallels. Scale is true along the standard parallels and constant between two parallels equidistant from the Equator. This projection is not equidistant. External links http www.radicalcartography.net ?projectionref Table of examples and properties of all common projections , from radicalcartography.net http www.uff.br mapprojections Behrmann en.html An interactive Java Applet to study the metric deformations of the Berhrmann Projection . Category Cartographic projections cartography stub cs Behrmannovo zobrazen ... more details
disambig There are several projections used in maps carrying the name of Johann Heinrich Lambert Lambert cylindrical equal area projection preserves areas Lambert azimuthal equal area projection preserves areas Lambert conformal conic projection preserves angles, commonly used in aviation navigation maps ... more details
File Equirectangular projection SW.jpg 450px thumb Equirectangular projection of the world the standard parallel is the equator plate carr e projection . Image Tissot indicatrix world map equirectangular proj.svg thumb right 450px The equirectangular projection with Tissot s indicatrix of deformation The equirectangular projection also called the equidistant cylindrical projection , geographic projection , or la carte parall logrammatique projection , and which includes the special case of the plate carr e projection or geographic projection , is a simple map projection attributed to Marinus of Tyre , who Ptolemy claims invented the projection about 100 AD 100 . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp. 5 8, ISBN 0 226 76747 7. ref The projection ... straight lines of constant spacing for constant intervals of Circle of latitude parallels . The projection is neither equal area nor Conformal map projection conformal . Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its ... of the equator where the scale of the projection is true math x math is the horizontal position ... of the resulting projection. The lang fr plate carr e French language French , for square plate , is the special case where math scriptstyle varphi 1 math is zero. This projection maps math x math to be the value ... called the latitude longitude or lat lon g projection or is said erroneously to be unprojected . See also Portal Atlas Cartography Cassini projection Gall Peters projection with resolution regarding the use of rectangular world maps Mercator projection Panorama References Reflist External links ... Panoramic Equirectangular Projection , PanoTools wiki. Map Projections Category Cartographic ... cil ndrica equidistante fr Projection cylindrique quidistante nl Equidistante cilinderprojectie ... simple Equirectangular projection uk ... more details
Population projection , in the field of demography , is an estimate of a future population. In contrast with intercensal estimates and censuses, which usually involve some sort of field data gathering, projections usually involve mathematical models based only on pre existing data. A projection may be made by a governmental organization, or by those unaffiliated with a government. See also Census Unreferenced date November 2010 DEFAULTSORT Population Projection Category Demography statistics stub fr Projection d mographique kk lt Demografin prognoz ru ... more details
File Collignon projection SW.jpg 450px thumb Collignon projection of the world. The Collignon projection is an equal area Map projection Pseudocylindrical pseudocylindrical map projection first known to be published by douard Collignon in 1865 and subsequently cited by A. Tissot in 1881 . For the smallest choices of the parameters chosen for this projection, the sphere may be mapped either to a single diamond, a pair of squares or a triangle. Another projection that maps each hemisphere to a square is the quincuncial map . It is used in the polar areas as part of the HEALPix spherical projection, which is widely used in physical cosmology in making maps of the cosmic microwave background , in particular by the WMAP and future Planck Surveyor space missions. External links http www.progonos.com furuti MapProj Normal ProjPCyl projPCyl.html Collignon Pseudocylindrical Projections Collignon Projection , Carlos A. Furuti http melusine.eu.org syracuse mluque mappemonde doc collignon collignon.html Projection COLLIGNON m ridiens et parall les rectilignes , Manuel Luque, Giuseppe Matarazzo http www.uff.br mapprojections Collignon en.html An interactive Java Applet to study the metric deformations of the Collignon Projection . Category Cartographic projections Category Equal area projections cartography stub ... more details
File Bonne projection SW.jpg 450px thumb Bonne projection of the world, standard parallel at 45 N. A Bonne projection is a pseudoconical equal area map projection , sometimes called a d p t de la guerre or a Sylvanus fact date May 2012 projection. Although named after Rigobert Bonne 1727 1795 , the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter s usages were approximate, however, and it is not clear they intended to be the same projection. ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp.60 62, ISBN 0 226 76747 7 ref The projection is math x rho sin E , math math y cot varphi 1 rho cos E , math where math rho cot varphi 1 varphi 1 varphi , math math E frac lambda lambda 0 cos varphi rho math and &phi is the latitude, &lambda is the longitude, &lambda sub 0 sub is the longitude of the central meridian, and &phi sub 1 sub is the standard parallel of the projection ... geography central meridian and the standard latitude shapes are not distorted. The inverse projection ... varphi 1 math . Special cases of the Bonne projection include the sinusoidal projection , when &phi sub 1 sub is zero, and the Werner projection , when &phi sub 1 sub is &pi 2. The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection an alternative intermediate would be a Bottomley projection ref http www.cybergeo.eu index3977.html Between the Sinusoidal projection and the Werner an alternative to the Bonne , Henry ... article http exchange.manifold.net manifold manuals 5 userman mfd50Bonne.htm Bonne Map Projection ... Java Applet to study the metric deformations of the Bonne Projection http mathworld.wolfram.com BonneProjection.html Bonne Projection wolfram.com DEFAULTSORT Bonne Projection Category Cartographic projections Category Equal area projections Cartography stub es Proyecci n de Bonne fr Projection ... more details
The Littrow projection is the only conformal retroazimuthal map projection . A retroazimuthal projection is one in which the direction to a fixed location B the bearing at the starting location A of the shortest route corresponds to the direction on the map from A to B. The Littrow projection allows direct measurement of the azimuth from any point on the map. The Littrow projection was created in 1833 by Joseph Johann Littrow 1781 1840 . It is sometimes referred to as a Weir Azimuth diagram . External links http www.csiss.org map projections Azimuthal.html A Gallery of Map Projections Azimuthals & Related http www.csiss.org map projections Azimuthal Littrow.pdf Littrow map http www.uff.br mapprojections Littrow en.html An interactive Java Applet to study the metric deformations of the Littrow Projection . Cartography stub Category Cartographic projections ... more details
views Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three dimensional space to points on a two dimensional projection plane . The projected point on the plane is chosen such that it is Line geometry collinear with the corresponding three dimensional point and the centre of projection . The lines connecting these points are commonly referred to as projectors . The centre of projection can be thought of as the location of the observer while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed e.g., photographic negative, photographic print, computer monitor . When the centre of projection is at a finite distance from the projection plane, a Perspective graphical perspective projection is obtained. When the centre of projection is at infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections . Mathematical formulation Mathematically, planar projections are linear transformations acting on a point in three dimensional space math mathbf a x,y,z math to give a point math mathbf b u,v math on the projection plane. These transformations consist of various function composition compositions of the five transformations orthographic projection , rotation mathematics rotation , Shear mapping shear , Translation geometry translation and Projective transformation perspective . Map uses It is also used in maps to show the planet Earth and other planets or objects in space. This is good for maps of close up areas. Category Graphical projections geometry stub ... more details
Main Conformational isomerism style border 1px solid AAA float right margin left 10px colspan 2 Molecule of butane in syn clinal sc conformation align center Image Sawhorse projection butane sc.png 120px align center Image Newman projection butane sc.png align center Sawhorse br projection align center Newman br projection A Newman projection , useful in alkane stereochemistry , visualizes chemical conformation s of a carbon carbon chemical bond from front to back, with the front carbon represented by a dot and the back carbon as a circle see below . The front carbon atom is called proximal , while the back atom is called distal . This type of representation is useful for assessing the torsional angle between bonds. A Sawhorse representation , on the other hand, views a carbon carbon bond from an oblique angle. This type of representation makes it easy to visualize the molecule as a whole in 3 D. Other methods for depicting molecules are the Fischer projection , the Haworth projection and the Natta projection . This projection is named after Melvin Spencer Newman , an American chemist of Ohio State University who introduced it in 1952. References Newman, M. S. Record. Chem. Progr. Kresge Hooker Sci. Lib. 1952 , 13 , 111. Newman, M. S. A notation for the study of certain stereochemical problems. J. Chem. Educ. 1955 , 32 , 344 347. See also commons category Newman projection Haworth projection Fischer projection Natta projection Category Stereochemistry ar de Newman Projektion es Proyecci n de Newman fr Projection de Newman it Proiezione di Newman he hu Newman projekci nl Newmanprojectie ja pl Projekcja Newmana ru sv Newmanprojektion zh ... more details
Image proj map.png thumb right Commutativity of this diagram is the universality of projection , for any map f and set X. Generally speaking, in mathematics , a projection is a mapping of a Set mathematics set or of a structure mathematics mathematical structure which is idempotent , which means that a projection is equal to its Function composition composition with itself. A projection may also refer .... Originally, the notion of projection was introduced in Euclidean geometry to denotes the projection ... are The projection from a point onto a plane or central projection If C is the point, called center of projection , the projection of a point P different of C is the intersection with the plane ... any image by the projection. The projection onto a plane parallel to a direction D The image of a point ... other projections, called projection map s have been defined for the need of cartography. The 3D projection ... the two kinds of projections and of defining the image by a central projection of any point different of the center of projection are at the origin of projective geometry . The original notion of projection has been extended or generalized to various mathematical situations, frequently, but not always ... sup projection set theory projection map , written proj sub j sub , that takes an element x ... equivalence relation is known as the canonical projection. The evaluation map sends a function f ... product math prod i in X Y i math , and the evaluation map is a projection map from the cartesian ... a canonical projection morphism to each factor. This projection will take many forms in different categories. The projection from the Cartesian product of set mathematics sets , the product topology ..., the mapping that takes a point x , y , z in three dimensions to the point x , y , 0 in the plane is a projection. This type of projection naturally generalizes to any number of dimensions n for the source and k n for the target of the mapping. See orthogonal projection , projection linear algebra . In the case ... more details
Refimprove date February 2012 A projection clock also called ceiling clock is an analog signal analog or digital clock equipped with a Image projector projector that creates an enlarged image of the clock face on any suitable projection screen , most often the ceiling. The advantage of a projection clock is that the clock can be placed almost anywhere. Depending on the projector used, the image can be in monochrome or color. The image generated by most projection clocks is large enough that a nearsightedness nearsighted person can see it from distance without glasses or contact lenses. Projection clocks are also used in advertising and merchandising . High brightness analog projection clocks can superimpose a business logo on top of the clock face, while there are low brightness projection clocks designed for home use that project for example a logo in addition to the time. Projection clocks may be connected to and synchronize with an Atomic clock to self adjust their time accurately. History Projection clocks were patented at least twice once in 1909, and another time in 1940. ref http www.roger russell.com project project.htm Dead link date February 2012 ref Both patents have expired by now. Early projection clocks were universally analog but with the widespread adoption of digital clocks, digital projection clocks became the standard. Technology A projection clock usually needs a backlight like an incandescent light bulb incandescent bulbs or light emitting diode LEDs . There are low brightness and high brightness clocks. While the projection created by low brightness clocks ... indoor places. Low brightness projection clocks Most modern projection clocks use a red ... reading when ambient light is too bright for the projection to be seen. They are often integrated into alarm clocks. High brightness projection clocks Modern high brightness projection clocks are in most ... to combine analog and digital information on the projected image. Projectors used in projection ... more details
Image Usgs map albers equal area conic.PNG frame right An Albers projection shows areas accurately, but distorts shapes. File Albers projection SW.jpg 450px thumb Albers projection the world, standard parallels 20 N and 50 N. The Albers equal area conic projection , or Albers projection named after Heinrich C. Albers , is a Map projection Conical conic , Map projection Equal area equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels. The Albers projection is the standard projection for British Columbia . ref cite web title British Columbia Map Projection Standard publisher BC Integrated Land Management Bureau url http www.ilmb.gov.bc.ca risc pubs other mappro map.htm accessdate 2010 08 05 ref It is also used by the United States Geological Survey and the United States Census Bureau . ref cite web title Projection Reference publisher Bill Rankin url http www.radicalcartography.net ?projectionref accessdate 2009 03 31 ref Snyder ref name snyder Cite book author Snyder, John P. title Map Projections &ndash A Working Manual. U.S. Geological Survey Professional Paper 1395 publisher United States Government Printing Office, Washington, D.C. year 1987 This paper can be downloaded from http pubs.er.usgs.gov pubs pp pp1395 USGS pages. ref Section 14 describes generating formul for the projection, as well as the projection s characteristics. Formul also appear at http mathworld.wolfram.com AlbersEqual AreaConicProjection.html Mathworld s page on the Albers projection . References ... s page on the Albers projection http www.radicalcartography.net ?projectionref Table of examples and properties ... geomatics techweb yt albers projection.html Yukon Albers Projection http www.uff.br mapprojections Albers en.html An interactive Java Applet to study the metric deformations of the Albers Projection ... fr Projection d Albers nl Projectie van Albers pt Proje o de Albers ru ... more details
Image Bottomley projection.gif thumb 250px right A Bottomley projection A Bottomley projection is an equal area map projection . The projection is math x frac rho sin E sin phi 1 , math math y tfrac pi 2 rho cos E , math where math rho tfrac pi 2 phi , math math E frac lambda sin phi 1 sin rho rho math and &phi is the latitude, &lambda is the longitude from the central meridian, and &phi sub 1 sub is the given parallel of the projection which determines its shape, all in radians. Parallels i.e. lines of latitude are concentric ellipse elliptical arcs of constant eccentricity mathematics eccentricity , centred on the north pole . On the central meridian geography meridian , shapes are not distorted, but elsewhere they are. Different projections can be produced by altering the eccentricity of the arcs, making it vary between the sinusoidal projection and the Werner projection . It was introduced by Henry Bottomley as an alternative to the Bonne projection to reduce the extent of extreme distortion at the edges and give a more satisfying overall shape. External links http www.cybergeo.eu index3977.html Cybergeo article Category Cartographic projections Category Equal area projections Cartography stub ... more details
Refimprove date September 2009 Views Parallel projections have lines of projection that are parallel both in reality and in the projection plane. Clarify date November 2009 Parallel projection corresponds to a perspective projection with an infinite focal length the distance from the image plane to the projection point , or zoom lens zoom . Within parallel projection there is an ancillary category ... for economy of effort and best effect. Orthographic projection File Camera focal length distance.gif thumb right Parallel projection corresponds to a perspective projection with a hypothetical viewpoint ... length, or zoom . The orthographic projection is derived from the principles of descriptive geometry , and is a type of parallel projection where the projection rays are perpendicular to the projection ... 6&ved 0CBoQ6AEwBQ v twopage&q axonometric 20orthographic&f false isbn 0801472806 ref It is the projection ... with the projection plane paper on which the Orthographic or parallel projection is drawn. ref name maynard Pictorials Axonometric projection Axonometric projection is a type of orthographic projection where the plane or axis of the object depicted is not parallel to the projection plane, ref name ... projection , depending on the exact angle at which the view deviates from the orthogonal. ref ... of space is usually displayed as vertical. File Graphical projection comparison.png thumb right Comparison of several types of graphical projection . Isometric projection In isometric pictorials for protocols see isometric projection , the most common form of axonometric projection, ref name godse ... to perceive. fact date November 2009 Dimetric projection In dimetric pictorials for protocols see dimetric projection , the direction of viewing is such that two of the three axes of space appear ... are common in dimetric drawings. Trimetric projection In trimetric pictorials for protocols see trimetric projection , the direction of viewing is such that all of the three axes of space ... more details
Projection pursuit is a type of statistical technique which involves finding the most interesting possible projections in multidimensional data. Often, projections which deviate more from a Normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections this is the pursuit aspect that motivated the technique known as matching pursuit . The projection pursuit concept was developed by Jerome H. Friedman and John Tukey in 1974. See also Projection pursuit regression Targeted projection pursuit References cite journal title A Projection Pursuit Algorithm for Exploratory Data Analysis author J. H. Friedman and J. W. Tukey journal IEEE Transactions on Computers month Sep. year 1974 volume C 23 issue 9 pages 881 890 issn 0018 9340 url http www.slac.stanford.edu cgi wrap getdoc slac pub 1312.pdf doi 10.1109 T C.1974.224051 cite journal title Projection pursuit author P. J. Huber journal The Annuals of Statistics month Jun. year 1985 volume 13 issue 2 pages 435 475 url http www.stat.rutgers.edu rebecka Stat687 huber.pdf doi 10.1214 aos 1176349519 cite journal doi 10.2307 2981662 author M. C. Jones and R. Sibson title What is Projection Pursuit? journal Journal of the Royal Statistical Society, Series A General year 1987 volume 150 issue 1 pages 1 37 jstor 2981662 Category Exploratory data analysis Category Multivariate statistics stat stub de Projection Pursuit fr Poursuite de projection ru ... more details
File Cassini projection SW.jpg thumb Cassini projection of the world. The Cassini projection is a map projection described by C sar Fran ois Cassini de Thury in 1745 . ref Flattening the Earth Two Thousand Years of Map Projections , John P. Snyder, 1993, pp. 74 76, ISBN 0 226 76747 7. ref It is the Transversality transverse aspect of the equirectangular projection , in that the globe is first rotated so the central meridian becomes the equator , and then the normal equirectangular projection is applied. Composing these operations math x arcsin cos phi sin lambda , math math y arctan left frac tan phi cos lambda right math where math lambda math is the longitude from the central meridian and math phi math is the latitude. When programming these equations, the inverse tangent function used is actually the atan2 function, with the first argument math sin phi math and the second math cos phi cos lambda math . The use of the Cassini projection has largely been superseded by the Transverse Mercator projection, at least with central mapping agencies. Distortions Things along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north south direction, and varies by the square of the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes. Due to this, the Cassini projection works best on long, narrow areas, and worst on wide areas. References references External links http www.radicalcartography.net ?projectionref Table of examples and properties of all common projections , from radicalcartography.net http www.ordnancesurvey.co.uk oswebsite freefun geofacts geo1164.html Ordnance Survey GeoFacts on the Cassini Projection DEFAULTSORT Cassini Projection Category Cartographic projections Cartography stub ... more details
Other uses Projection disambiguation Views Image Convention placement vues dessin technique.svg thumb right 200px Symbols used to define whether a projection is either Third Angle right or First Angle left . Graphical projection is a protocol by which an image of a Three dimensional space three dimensional ... the focal length and distance of the camera to infinity in a perspective projection results in a parallel projection. The projection is achieved by the use of imaginary projectors . The projected ... projection, categories each with its own protocol parallel projection Perspective graphical perspective projection gallery widths 100px heights 100px align center style padding 0px Image Isometrie.png Isometric projection . Image Milit rperspektive.PNG Oblique projection . Image Cavalier perspective 45.svg Oblique projection . Image Zentralperspektive.png Vanishing point One point perspective projection . gallery Types of projection File Graphical projection comparison.png thumb right Several types of graphical projection compared. Parallel projection In parallel projection , the lines of sight from the object to the projection plane are parallel to each other. Within parallel projection there is an ancillary ..., some liberties may be taken for economy of effort and best effect. Orthographic projection The Orthographic projection is derived from the principles of descriptive geometry and is a two dimensional representation of a three dimensional object. It is a parallel projection the lines of projection are parallel both in reality and in the projection plane . It is the projection type of choice for Plans drawings working drawings . Pictorials Axonometric projection main Axonometric projection Within parallel projection there is a subcategory known as Pictorials . Pictorials show an image of an object .... Parallel projection pictorial instrument drawings are often used to approximate graphical perspective ... then be taken for economy of effort and best effect. Parallel projection pictorials rely on the technique ... more details
Image Dot Product.svg thumb 300px right If 0 90 , as in this case, the scalar projection of a on b coincides with the Euclidean norm length of the vector projection . File Projection and rejection.png thumb 200px Vector projection of a on b a sub 1 sub , and vector rejection of a from b a sub 2 sub . The scalar projection of a vector geometric vector math mathbf a math on or onto a vector math mathbf b math , also known as the scalar resolute or scalar component of math mathbf a math in the direction of math mathbf b math , is given by math s mathbf a cos theta mathbf a cdot mathbf hat b , math where the operator math cdot math denotes a dot product , math hat mathbf b math is the unit vector in the direction of math mathbf b math , math mathbf a math is the Euclidean norm length of math mathbf a math , and math theta math is the angle between math mathbf a math and math mathbf b math . The scalar projection is a scalar mathematics scalar , equal to the Euclidean norm length of the orthogonal projection of math mathbf a math on math mathbf b math , with a minus sign if the projection has an opposite direction with respect to math mathbf b math . Multiplying the scalar projection of math mathbf a math on math mathbf b math by math mathbf hat b math converts it into the above mentioned orthogonal projection, also called vector projection of math mathbf a math on math mathbf b math ... b math is known, the scalar projection of math mathbf a math on math mathbf b math can be computed ... projection math s , math becomes math s mathbf a cos theta mathbf a frac mathbf a cdot mathbf b mathbf a , mathbf b frac mathbf a cdot mathbf b mathbf b , math Properties The scalar projection has ... of the corresponding vector projection if the angle is smaller than 90 . More exactly, if the vector projection is denoted math mathbf a 1 math and its length math mathbf a 1 math math s mathbf a 1 math .... See also Scalar product Cross product Vector projection Category Vectors Mathanalysis stub ca Projecci ... more details
, see Projection linear algebra . Views Oblique projection is a simple type of graphical projection used ... projection yz.svg thumb left 240px Oblique projection with foreshortening by half, seen from the side. Oblique projection is a type of parallel projection it projects an image by intersecting parallel rays projectors from the three dimensional source object with the drawing surface projection plane . In both oblique projection and orthographic projection , parallel lines of the source object produce parallel lines in the projected image. The projectors in oblique projection intersect the projection ... angle used in orthographic projection. Mathematically, the parallel projection of the point math x, y ... b math uniquely specify a parallel projection. When math a b 0 math , the projection is said to be orthographic ... are not necessarily less than 1, and as a consequence lengths measured on an oblique projection may be either larger or shorter than they were in space. In a general oblique projection, spheres of the space ... an orthogonal projection. Oblique drawing is also the crudest 3D drawing method but the easiest ... overcome by aligning one plane of the image parallel to the plane of projection. Doing so creates .... Cavalier projection is the name of such a projection, where the length along the math z math axis remains ... from PlaneView3D Online ref Cabinet projection , popular in furniture illustrations, is an example ... projection sometimes cavalier perspective or high view point a point of the object is represented by three ... are drawn with a 1 1 scale it is thus similar to the dimetric projection s, although it is not an orthographic projection , as the third axis, here y , is drawn in diagonal, making an arbitrary angle ... Cabinet projection The term cabinet projection sometimes cabinet perspective stems from its use in illustrations ... as going off in an angle typical 30 or 45 . Unlike cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half. Mathematical formula ... more details
File Mollweide projection SW.jpg 450px thumb Mollweide projection of the world. Image Tissot indicatrix world map Mollweide proj.svg thumb 450px The Mollweide projection with Tissot s indicatrix of deformation The Mollweide projection is a Map projection pseudocylindrical map projection generally used for global maps of the world or sky . Also known as the Babinet projection , homalographic projection , homolographic projection , and elliptical projection . As its more explicit name Mollweide equal area projection indicates, it sacrifices accuracy of angle and shape in favor of accurate proportions ..., for instance small maps depicting global distributions. The projection was first published by mathematician .... It was popularized by Jacques Babinet in 1857, giving it the name homalographic projection . The variation ... as seen by the Wilkinson Microwave Anisotropy Probe . Projected using the Mollweide projection. Image ... Data Analysis Project . Projected using the Mollweide projection. The projection is math x frac ... be bypassed otherwise, division by zero may result. Properties The Mollweide is a Map projection Pseudocylindrical pseudocylindrical projection in which the equator is represented as a straight horizontal ..., although not as severe as in the sinusoidal projection . Shape distortion may be diminished by using an interrupted version. A sinusoidal interrupted Mollweide projection discards the central ... projection uses multiple disjoint central meridians, giving the effect of multiple ellipses ..., has inspired the creation of several other projections, including the Goode homolosine projection Goode s homolosine , van der Grinten projection van der Grinten and the Boggs eumorphic projection Boggs ... 252 ref See also Aitoff projection Hammer projection References reflist External links http www.uff.br ... and angle of the Mollweide Map Projection http mathworld.wolfram.com MollweideProjection.html Mollweide Projection at Mathworld Category Cartographic projections Category Equal area projections ca Projecci ... more details
Unreferenced stub auto yes date December 2009 Orphan date October 2008 Calligraphic projection is a system, often used for laser lighting display s, whereby one or more laser beams draws an image on a screen by reflecting the laser beam from one or more mirrors attached to a deflecting mechanism. Analog oscilloscope s have customarily employed this kind of vector graphics , as did a number of computer graphics terminals in the 1970s, such as the Tektronix 4014 . Calligraphic projection is sometimes called Jules Antoine Lissajous Lissajous projection, after the mathematical figure and mathematician . See also Lissajous curve calligraphy DEFAULTSORT Calligraphic Projection Category Entertainment Category Laser image generation Compu graphics stub Optics stub ... more details
hatnote For use in map making, see Orthographic projection cartography . Views Orthographic projection or orthogonal projection is a means of representing a Three dimensional space three dimensional object in Two dimensional two dimensions . It is a form of parallel projection , where all the projection lines are orthogonal to the projection plane, ref name maynard Cite book last Maynard first Patric ... projections and axonometric projection s . A lens providing an orthographic projection is known ... of the object is also parallel with the projection plane, ref name maynard as in multiview orthographic ... to define whether a projection is either Third Angle right or First Angle left . Origin The orthographic projection has been known since antiquity, with its cartographic uses being well documented. Hipparchus used the projection in the 2nd century B.C. to determine the places of star rise and star set. In about 14 B.C., Roman engineer Vitruvius Marcus Vitruvius Pollio used the projection to construct ... orthos straight and graph drawing for the projection. However, the name analemma , which also ... promoted its present name in 1613. ref name Snyder16 The earliest surviving maps on the projection ... orthographic projection With multiview orthographic projections, up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views ... projection. In each, the appearances of views may be thought of as being projected onto planes that form ... view and right side view. Pictorials main Axonometric projection Within orthographic projection ... of effort and best effect. Orthographic pictorials rely on the technique of axonometric projection ... projection Multiview orthographic projection Orthographic projection cartography Telecentric lens Telephoto lens Orthographic projection geometry div col end References Reflist External links http www.3doro.de ... marine navigation orthographic projection.html Orthographic Projection Video and mathematics visualization ... more details
Unreferenced date December 2009 The Projection Principle is a stipulation proposed by Noam Chomsky as part of the Phrase Structure Component of Generative grammar Generative Transformational Grammar . Under the Projection Principle, the properties of lexical items must be preserved while generating the phrase structure of a sentence. The Principle, as formulated by Chomsky in Knowledge of Language Its Nature, Origin and Use 1986 , states that lexical structure must be represented categorically at every syntactic level . For example, the verb strangle , apart from the subject, has an obligatory argument, its object, which must appear in the sentence. The following subcategorization frame for the verb strangle specifies its properties the underlined gap for the location of the verb is followed by the noun phrase NP strangle Verb, NP It is out of this frame that a sentence like the following can be generated Fabio strangled Prince Jamal. A sentence without the object, in violation of the verb s subcategorization frame and the Projection Principle, would be ill formed sup sup Fabio strangled. Before the Projection Principle was proposed, phrase structures were generated in separation from the properties of lexical entries. These were hypothesized to enter the slots in pre generated structures waiting to be filled by the lexical material. According to more recent theories, phrase structures are not generated by phrase structure rules, but are projected from the lexical entries. The Projection Principle therefore obviates the need for phrase structure rules in the generative component. Category Grammar Category Noam Chomsky de Projektionsprinzip fr Principe de projection pa projection principle ... more details
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